工程力学 ›› 2016, Vol. 33 ›› Issue (12): 186-195.doi: 10.6052/j.issn.1000-4750.2015.04.0423

• 土木工程学科 • 上一篇    下一篇

基于裂纹诱导弦挠度的Timoshenko梁裂纹无损检测

汪德江, 杨骁   

  1. 上海大学土木工程系, 上海 200072
  • 收稿日期:2015-04-23 修回日期:2016-01-11 出版日期:2016-12-25 发布日期:2016-12-25
  • 通讯作者: 汪德江(1970-),男,山东烟台人,讲师,博士,从事结构计算理论、大跨度结构分析研究(E-mail:djwang@shu.edu.cn). E-mail:djwang@shu.edu.cn
  • 作者简介:杨骁(1965-),男,山西运城人,教授,博士,从事结构非线性分析、结构加固与修复研究(E-mail:xyang@shu.edu.cn).

CRACK NON-DESTRUCTIVE TEST IN TIMOSHENKO BEAMS BASED ON CRACK-INDUCED CHORD-WISE DEFLECTION

WANG De-jiang, YANG Xiao   

  1. Department of Civil Engineering, Shanghai University, Shanghai 200072, China
  • Received:2015-04-23 Revised:2016-01-11 Online:2016-12-25 Published:2016-12-25

摘要: 研究了基于Timoshenko梁静态挠度识别梁中裂纹位置及损伤程度的计算方法。首先,将梁开闭裂纹等效为单向旋转弹簧,利用Delta函数和Heaviside函数,得到了具有任意开闭裂纹数目梁的等效抗弯刚度,求得了开闭裂纹Timoshenko梁弯曲变形的显式闭合通解,给出了闭合通解待定常数的迭代求解方法。其次,建立了裂纹诱导弦挠度函数,证明了在裂纹处裂纹诱导弦挠度曲线斜率存在突变,为裂纹位置识别提供了理论依据。在此基础上,给出了裂纹等效旋转弹簧刚度的近似计算公式。最后,通过数值试验,将所建立的方法分别应用于裂纹位置及损伤程度已知的简支和固支Timosheoko梁裂纹位置识别和损伤程度计算,结果表明该文建立的裂纹损伤识别方法不仅具有一般的适用性,而且具有较高的精度和可靠性。

关键词: Timoshenko梁, 无损检测, 闭合解, 开闭型裂纹, 裂纹缝隙, 广义函数

Abstract: A method for crack position identification and crack-damage evaluation in cracked Timoshenko beams using beam's static deflection was proposed. At first, representing a switching crack with gap as a unidirectional rotational spring, the equivalent flexural rigidity of the beam with arbitrary number of switching cracks was presented by the generalized Delta function and the Heaviside function. The general explicit closed-form solution for the bending of the cracked Timoshenko beams was derived, and an iteration method for determining unknown constants of the closed-form solution was given. Subsequently, the crack-induced chord-wise deflection function was proposed, and it was proven that there existed an abrupt change in the slope of the crack-induced chord-wise deflection curve at the crack location, which provided the theoretical basis for crack position identification. On this basis, an approximate formula of the equivalent rotational spring rigidity of the crack was given. Finally, the proposed methodology was applied to crack position identification and crack-damage evaluation of simply-supported and clamped cracked Timoshenko beams with known crack locations and crack-damage levels, respectively, by means of numerical experiment It has been demonstrated that the proposed methodology for crack-damage identification not only has the general validity, but also a high level of precision and reliability.

Key words: Timoshenko beam, non-destructive test, closed-form solution, switching crack, crack gap, generalized function

中图分类号: 

  • TU317
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